Line a large baking sheet with parchment paper and set aside.
In a large bowl, combine the crabmeat, mayo, mustard, capers, parsley, dill, lemon zest, cajun seasoning, salt, and pepper. Use a fork to mix until combined, breaking up and larger chunks of crab. Add the panko and stir once more to combine.
Use a 1/3-cup measuring cup to scoop out the crab mixture and, using your hands, form into a patty. Set on the prepared baking sheet and continue until all of the crab cakes are formed. Refrigerate for about 10 minutes while you prepare the dressing.
Make the Vinaigrette:
In a blender or using an immersion blender in a wide mouth jar, combine all of the champagne vinaigrette ingredients and blend until just smooth. Set aside.
Cook the Crab Cakes:
In a large nonstick skillet, heat the oil over medium heat. When the oil is hot, but not yet smoking, use a sturdy spatula to carefully lay the crab cakes into a single layer in the hot oil. You will likely need to do this in two batches to not overcrowd the pan. Cook until golden brown on both sides, 3 to 4 minutes per side. Transfer the cooked crab cakes to a wire baking rack to prevent them from softening.
Assemble the Salads:
To serve, divide the lettuce among 4 plates and drizzle each with desired amount of the Champagne Vinaigrette. Add two crab cakes per plate and top with fresh dill.